Many vertebrates, forest herbs, and trees exhibit both variable age at maturity and iteroparity as adaptations to uncertain environments. We analyze a stochastic model that combines these two life-history adaptations with density-dependent fertility. Results for a model with only iteroparity are consistent with previous work; environmental uncertainty favors adult survival over juvenile survival. This holds true even if there is a moderately strong convex trade-off between adult survival and fecundity, but the direction of selection can depend on which life-history trait is considered a random variable. A life history with only developmental delay favors juvenile survival in uncertain environments, consistent with previous models of seed banks. When both developmental delay and iteroparity are included in the model, both adaptations are favored in uncertain environments. Our simulations show that selection is not necessarily a runaway process in which either developmental delay or iteroparity is favored, as recently proposed by Tuljapurkar and Wiener, but rather that selection can favor both mechanisms. Invasion analysis shows that selective pressure on life-history delays increases as environmental variation increases. Reproductive delay and adult survival can be either adaptations or constraints. Natural-history studies that estimate model parameters can resolve this uncertainty.